论文标题
优化流登陆处于stiefel歧管上
Optimization flows landing on the Stiefel manifold
论文作者
论文摘要
我们研究了一个连续的时间系统，该系统解决了整个正顺序矩阵的优化问题，该系统也称为Stiefel歧管。产生的优化流程遵循的路径并非总是在流形上，而是渐近地降落在歧管上。我们介绍了一个广义的stiefel歧管，我们将其扩展了Stiefel歧管的规范指标。我们表明，所提出的流量的向量场可以解释为在广义的stiefel歧管和正常载体上的riemannian梯度之和。此外，我们证明了所提出的流动在全球范围内收敛到临界点集，任何局部最小值和孤立的临界点都是渐近稳定的。
We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization flow follows a path that is not always on the manifold but asymptotically lands on the manifold. We introduce a generalized Stiefel manifold to which we extend the canonical metric of the Stiefel manifold. We show that the vector field of the proposed flow can be interpreted as the sum of a Riemannian gradient on a generalized Stiefel manifold and a normal vector. Moreover, we prove that the proposed flow globally converges to the set of critical points, and any local minimum and isolated critical point is asymptotically stable.
